In the physical sense, the "silver lining" of a cloud is the edge, where the sun's rays can shine through the thinnest part of the cloud and give it a radiant, glowing appearance (as opposed to the rest of the cloud, which blocks out the sunlight and looks anywhere from dull-white to dark grey).
As far as the film title, I haven't seen nor heard of it, but I assume that it is about a set of methods that allow you to make the best of a bad situation; in other words, a "playbook of silver linings", which may also be expressed as a Silver Linings Playbook; it is not a "playbook belonging to silver linings" (which is what it would have to be to be called Silver Linings' Playbook).